I am searching for good spots to gather ingredients, preferably outside locations around Riften.

Inside riften and the docks, lots of salt in barrels.

good fish in the lake west of riften, and some nirnroots.

lots of bees outside a bear cave near ivarstead.

north of riften towards Shor's stone, roadside flowers and butterflies.

keep going north toward windhelm, lots of creep clusters, dragon flowers and jazbay graqes in the hot springs area.

Marshes in the north are good.

Your best bet for this is to check Wikia and/or UESP because there are ingredients everywhere that differ by region and there's no short answer unless you're looking for something specific.

If you Fus Ro Dah the lake area outside the Riften walls you'll get every kind of fish floating to the surface, and the two kinds of dragonflies sinking to the bottom - although I prefer swimming and just collecting the fish on a bright sunny day. Very pleasant.